What does that mean? Is it high? Should we do better? It turns out the answers to those questions tell us that U.S. income redistribution policies go too far towards helping the poor, and are too harsh on the middle class.

So what does the 76% mean? As typical in income inequality work, we’re dealing with quintiles of the population. And Mankiw’s numbers come from this report (also used for class in this post), with his calculation motivated by this op-ed piece. The report is important because it is currently the most comprehensive analysis of income, in that it counts more additions to income (like social programs) and subtractions from income (like taxes) than any other source. For example, it shows in its Table 4 that the lowest quintile takes home 2.2% of the income earned across the country (that’s the sense in which we have an income inequality problem), but after counting all other changes to their income they end up with 12.9% of the income (that improvement is the sense in which our social programs are helping the poor). That last number is called Final Net Income After All Taxes and Transfers (FNIAATT).

Mankiw then asks a question that’s been bugging some economists for a while: is it worth it for a poor person to try and not be poor? The problem here is that to improve their lot the poor must earn more income. But in doing so, they often lose out on a lot of benefits, and pay somewhat higher taxes. For example, if they worked more hours, and earned 60% more income, but lost 42% of their starting net income by losing some benefits, they’d only be up 18% because an effective marginal tax rate of 70% took the rest away (that’s one minus the difference of 60 and 42 divided by 60).

The hobgoblin making that happen is usually means testing. This is the idea that we should help the poor more than the not-quite-so-poor because the poor need more help. It sounds efficient, and it definitely reduces the size of transfer programs. But it also means when someone is climbing the ladder of success, the government is kicking at them from above.

Mankiw then does something a little goofy (I’m not sure if this is a feature or a bug). He doesn’t calculate the effective marginal tax rate from the lowest quintile to the second lowest, but rather from the lowest to the middle one. Whatever, it’s not a big deal. Here’s what he finds. The share of FINAATT for the middle quintile is 15.4%, so the improvement is 2.5%. But the share of income earned in the market by the middle quintile is 12.6%, so the improvement is 10.4%. Here’s the thing: the people in the middle worked more, harder, or better to get that 10.4%, but lost most of it as taxes and transfers changed leaving them with just 2.5% — 76% of what they worked more, harder, or better for was taken away. That answers my first question. If you’re interested in the less-goofy question about going up from the lowest to the second lowest quintile, the rate is a tad higher at 79%.

On the face of it, that’s sounds like a huge discouragement to work more, harder, or better. Let’s not be so hasty. Most of us are comfortable living in a society in which at least something is transferred from the richer to the poorer. So we shouldn’t expect that number to be zero. And, we’re pretty used to paying a chunk of our income in federal income tax, having FICA withdrawn from our paychecks, sending more to states and localities in income and real estate taxes, and then paying sales taxes on top of that. Total those up, and you’re in the 40% range for many people. Note that this is an average rate: the math gets a little arcane, but effective marginal rates can diverge quite a bit from average rates, and a progressive tax system puts them on the high side. The bottom line is that we shouldn’t jump too quickly to presuming that my 79% (or Mankiw’s 76%) is too high.

A better way to assess this would be to figure out the effective marginal tax rates for all upward shifts. So, it’s 79% to go from lowest to second lowest, and then 73% to make the jump from second lowest to the middle quintile, 59% to go one step further, and then 44% to go from the second highest to the highest quintile. Now we’re getting somewhere. Our system as it currently stands punishes everyone for working more, harder, and better. But don’t forget that this is OK: it means we’re all chipping in to help the less fortunate. The thing is, we punish the poor who work more, harder, and better more than we punish the upper middle class who choose to do that. Is it any wonder that there’s a perception that the upper middle class has more strivers?

That answers my second question. Yes, 79% is too much to take from the poor who are trying to improve their lot because we don’t take as much from those who are better off and trying to do the same thing.

The third question is mathematically tougher. How could we do better? Let’s start with not punishing poor people who try to improve their lots more than richer people who try and improve theirs. That means we need to figure out how to simultaneously change all of the FINAATT shares so that the sequence of four rates are all the same. Here’s what we’d get:

Quintile

Current FINAATT Share

Improved FINAATT Share

Lowest

12.9

12.9

Second

13.9

14.9

Third

15.4

17.1

Fourth

18.6

20.2

Highest

39.3

35.1

Note that the shares shown may not add up to 100% due to rounding.

With the shares on the right, no matter which quintiles you move up from, and no matter how many steps you go up, the effective marginal tax rate is always 60%. That’s right in the middle of the four rates noted above. Do note the calculations show that the FINAATT share of the lowest quintile should go up ever so slightly, but not by enough to round up to the next digit.

There’s something for almost everyone here. Democrats/Progressives will be happy to see that more is redistributed away from the highest quintile. Republicans/Conservatives will be happy to see that we’ve already helped the poor “enough”. And (at least in word) everyone likes to help the middle class (generally understood to be the middle three quintiles), and these numbers show that they need some help: in the range of a 10% improvement in their share. That’s $5-10K more per year for tens of millions of households across the country: in the range of a car payment, tuition, or a sweet family vacation.

This result is ironic. There are duel concerns about whether we help the poor the right amount, and whether the poor have appropriate incentives to improve their lot. It turns out that getting the incentives right for the poor is mostly about making the middle class more attractive.

This also goes some way towards explaining what some view as capriciousness on the part of middle-class voters. Many are perplexed at the numbers of the middle-class who voted both for Trump in 2016, and Obama in either of the two previous elections (and maybe even showed an interest in the maverick or third-party campaigns of Dean, Nader, McCain, Buchanan, Perot, or even Anderson). They say they’re hurting, but it’s been difficult to pin down how that could be. Now we know.